Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

Weighing Problem Resurected

16 replies to this topic

#1 Prime

Prime

Senior Member

• Members
• 872 posts
• Gender:Male
• Location:Illinois, US

Posted 23 February 2013 - 02:05 AM

You have a dozen (12) stones weighing a whole number of grams between 1 and 6 each. You can obtain one reference weight of your choosing.

What reference weight can you choose to be able to figure out the individual weights of the 12 stones using a balance device for any possibility that may exist therein?

For an encore: what is the maximum weight range of stones (1 to N) that you could solve using 2 reference weights of your choice? Provided you can have as many  stones as you need.

I don't believe, I have solved this one myself. We could make it a community project after the first question is answered.

HISTORICAL NOTE:

This problem originated on Brain Den. I constructed it based on Bonanova's problem Weighty  Thoughts: http://brainden.com/...4932--/?p=84107 few years ago.

Back then limited number of people participated. The solution found was for specific numbers in that problem (range 1 to 5) – not general. I'd like to give it another try.

• 0

Past prime, actually.

#2 ThunderCloud

ThunderCloud

• Members
• 102 posts
• Gender:Male
• Location:New England

Posted 23 February 2013 - 02:25 AM

I thought I had this one... but found a flaw in my reasoning. [solution withdrawn]

Edited by ThunderCloud, 23 February 2013 - 02:33 AM.

• 0

#3 CaptainEd

CaptainEd

Senior Member

• Members
• 1094 posts

Posted 23 February 2013 - 03:27 AM

First part: do we know that all weights between 1-6 are represented in the 12 stones? Or is it possible that we have, say, 12 stones each waiting 6?
• 0

#4 phil1882

phil1882

Senior Member

• Members
• 564 posts

Posted 23 February 2013 - 03:29 AM

Spoiler for

• 0

#5 ThunderCloud

ThunderCloud

• Members
• 102 posts
• Gender:Male
• Location:New England

Posted 23 February 2013 - 03:38 AM

You have a dozen (12) stones weighing a whole number of grams between 1 and 6 each. You can obtain one reference weight of your choosing.

What reference weight can you choose to be able to figure out the individual weights of the 12 stones using a balance device for any possibility that may exist therein?

For an encore: what is the maximum weight range of stones (1 to N) that you could solve using 2 reference weights of your choice? Provided you can have as many  stones as you need.

I don't believe, I have solved this one myself. We could make it a community project after the first question is answered.

HISTORICAL NOTE:

This problem originated on Brain Den. I constructed it based on Bonanova's problem Weighty  Thoughts: http://brainden.com/...4932--/?p=84107 few years ago.

Back then limited number of people participated. The solution found was for specific numbers in that problem (range 1 to 5) – not general. I'd like to give it another try.

Spoiler for One method, though a bit of a cheat...

• 0

#6 Prime

Prime

Senior Member

• Members
• 872 posts
• Gender:Male
• Location:Illinois, US

Posted 23 February 2013 - 03:45 AM

First part: do we know that all weights between 1-6 are represented in the 12 stones? Or is it possible that we have, say, 12 stones each waiting 6?

There is no guaranty what weights are present/absent in your collection. The only guaranty is that each of the stones weighs a whole number of grams between 1 and 6.

12 stones each weighing 6 grams is one of the variations we must account for.

• 0

Past prime, actually.

#7 CaptainEd

CaptainEd

Senior Member

• Members
• 1094 posts

Posted 23 February 2013 - 04:25 AM

I like T-cloud's cheat. It's not a reference weight, but just a found object that represents a difference. Good outside the box thinking!
• 0

#8 CaptainEd

CaptainEd

Senior Member

• Members
• 1094 posts

Posted 23 February 2013 - 04:32 AM

Part 2: you can have as many stones as you want. Which stones? Reference stones of my two chosen denominations? Or as many unknown stones?
• 0

#9 CaptainEd

CaptainEd

Senior Member

• Members
• 1094 posts

Posted 23 February 2013 - 04:36 AM

Part 2: you can have as many stones as you want. Which stones? Reference stones of my two chosen denominations? Or unknown stones?
• 0

#10 Prime

Prime

Senior Member

• Members
• 872 posts
• Gender:Male
• Location:Illinois, US

Posted 23 February 2013 - 04:42 AM

Part 2: you can have as many stones as you want. Which stones? Reference stones of my two chosen denominations? Or as many unknown stones?

For the part 2, you can have 2 reference weights of your choice, as many stones as you want in the weight range from 1 to N. (Must find the largest N and the 2 reference weights.)

Let's solve the first part first. No tricks, no cheating, no different interpretations of the OP. If there is an ambiguity, I'll clarify it.

• 0

Past prime, actually.

0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users